In this section we learn about prime factors and how to find a whole number's prime factors.
A prime factor of a number is a prime number, which is also a factor of that number.
Remember that a prime number \(p\) is a whole number that has exactly two factors (a.k.a divisors):
Given a whole number \(m\), a prime factor \(p\) of \(m\) is a factor of \(m\) which is also a prime number.
For instance one of the prime factors of \(12\) is \(3\), as \(3\) is a factor of \(12\) and \(3\) is a prime number; indeed we can write:
\[12 = 3\times 4\]
so \(3\) is a factor of \(12\) and since \(3\) is a prime number it is a prime factor of \(12\).
Given a whole number \(m\), we can list all of its prime factors, \(p_1,p_2,p_3,\dots \), using the following two steps:
In the following tutorial we learn how to find the prime factors of a whole number.
List all of the prime factors of each of the following whole numbers
State whether each of the statements that follow is true or false.
All whole numbers can be written as a product of its prime factors.
The method we learn here is based-on the fundamental theorem of arithmetic. In essence, it states:
All whole numbers greater than, or equal to \(2\), can be written as a product of its prime factors.
In the following tutorial we learn how to write a number as a product of prime factors, watch it now:
Write each of the following whole numbers as its product of prime factors: